This invention relates generally to high power lasers and, more particularly, to arrays of fiber amplifiers configured to produce a powerful composite beam. Typically, radiation emitting fibers are arranged in two-dimensional array, referred to as a side-by-side array (SBSA), in which the phases of emitters are controlled render them mutually coherent. The beams combine in the far field as they diverge and diffract, forming the composite beam. The performance of such arrays is, however, significantly limited by the necessarily low “fill factor” of the array. Even if the fibers, which are cylindrical in shape, are closely packed in a hexagonal pattern, the fill factor is reduced by the spaces between adjacent fibers. One measure of the optical performance of such an array is the Strehl ratio of the composite beam, defined as the ratio of the on-axis intensity of the beam to the on-axis intensity that would have been obtained with a diffraction limited optical system with the same aperture and total power at the same range. A Strehl ratio of unity or 100% is indicative of an ideal beam, but this cannot be achieved in an SBSA, especially a fiber array, because the fill factor is generally significantly lower than 100%. For a closely packed array of cylindrical fibers, the fill factor as calculated by simple geometry is
      π    /          (              2        ⁢                  3                    )        ,which is approximately 90.7%. If one also takes into account that the radiation from each fiber end has a centrally peaked, near Gaussian, profile the effective fill factor is even further reduced, to approximately 74%.
Although it is possible to improve the effective fill factor of a fiber array to some degree by the use of refractive and/or diffractive optics, ideally it would be desirable to eliminate the effect that fill factor has on the Strehl ratio of a composite beam. The present invention provides a way to accomplish this. Another common drawback of prior art techniques that simply detect and compensate for relative phase differences in multiple beams is that multiple feedback phase control loops tend to interact with undesirable results as the number of beams is scaled up. The present invention also overcomes this drawback.